To answer your questions in order:
1) You should not buy them at the same time unless you want to wait at least 6 months to get the clowns. The clownfish are nearly bullet proof and are a great starter fish that you may want to get early on because they are awesome

. Hosting anemones are more fragile and require a very stable environment in which to thrive, so it is generally recommended that you not try one until at least 6 months for the heartier ones (ie Entacmaea quadricolor).
2) Yes, some anemone's host clowns, and others do not. Also, certain anemones will only host certain species of clown, although in captivity those boundaries often get blurred. (ie the popular Amphiprion ocellaris being hosted by an Entacmaea quadricolor isn't found in nature, but relatively common in aquaria).
3) All hosting anemone's will get large. Even bubble tip anemone's can grow to well over a foot in diameter. The other common hosting anemone's seen in reef aquaria are long tentacle anemones (can grow to about 2 feet), carpet anemones (can grow to 3 feet), and sabae anemone's (Ive seen up to 1.5 feet, but don't know how large they get maximally).
4) Bubble tip anemone's are generally recommended as the best starter hosting anemone. They are heartier than the rest and more easily attained. You are much more likely to be able to find a captive-cloned RBTA or GBTA than the other hosting anemone's, which I would highly recommend. No reason to steal an anemone from the wild if it isn't necessary, and you already know those anemone's do well in aquariums.
If you go down this route, please do tons of research beforehand, and if you intend to keep the anemone in a 29gallon cube long term, best to probably make it a dedicated aquarium to the nem and the clowns. Good luck!